| Exam Board | Edexcel |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Topic | Circles |
| Type | Circle touching axes |
| Difficulty | Moderate -0.8 This is a straightforward C2 circle question with routine steps: (a) requires simple geometric reasoning that if a circle touches the x-axis at (4,0) with radius 5, the centre must be at (4,5); (b) is direct substitution into the circle equation formula; (c) uses the standard right-angled triangle formed by radius, tangent, and line from centre to external point, requiring only Pythagoras. All parts are textbook-standard with no problem-solving insight needed, making it easier than average but not trivial since part (c) requires recognizing the geometric setup. |
| Spec | 1.03d Circles: equation (x-a)^2+(y-b)^2=r^21.03e Complete the square: find centre and radius of circle |
\includegraphics{figure_12}
The circle $C$, with centre $(a, b)$ and radius 5, touches the $x$-axis at $(4, 0)$, as shown in Fig. 1.
\begin{enumerate}[label=(\alph*)]
\item Write down the value of $a$ and the value of $b$. [1]
\item Find a cartesian equation of $C$. [2]
\end{enumerate}
A tangent to the circle, drawn from the point $P(8, 17)$, touches the circle at $T$.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{2}
\item Find, to 3 significant figures, the length of $PT$. [3]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C2 Q42 [6]}}